Problem: You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

int a, b, k;

int main()
{
	cin >> a >> b >> k;
	if (b == 0)
		cout << "NO" << endl;
	else if ( k == 0) {
		cout << "YES" << endl;
		for (int i = 1; i <= b; i++)cout << 1;
		for (int i = 1; i <= a; i++)cout << 0;
		cout << endl;
		for (int i = 1; i <= b; i++) cout << 1;
		for (int i = 1; i <= a; i++)cout << 0;
		cout << endl;
	}
	else if (a + b-1 <= k) {
		cout << "NO" << endl;
	}
	else if (b == 1&&k!=0||a==0&&k!=0) {
		cout << "NO" << endl;
	}
	
	else {
		cout << "YES" << endl;
		int cc = 0;
		for (int i = 1; i <= b; i++) {
			if (i == 2 + k)
				cout << 0, cc++;
			else
			{
				cout << 1;
			}
		}
		if (cc) cout << 1;
		for (int i = 1; i <= a-cc; i++)cout << 0;
		cout << endl;
		for (int i = 1,cc=0; i <= a + b; i++) {
			if (i == 2)cout << 0;
			else if (i == 2 + k) {
				cout << 1;
				if (i <= b)cc++;
			}
			else if (i <= b  + cc)
				cout << 1;
			else cout << 0;
		}
		cout << endl;

	}

}